Certain new robust properties of invariant sets and attractors of dynamical systems

1999 ◽  
Vol 33 (2) ◽  
pp. 95-105 ◽  
Author(s):  
A. S. Gorodetski ◽  
Yu. S. Ilyashenko
Keyword(s):  
Dynamical Systems ◽  
Invariant Sets

scholarly journals Characteristic exponents of dynamical systems in metric spaces

1983 ◽  
Vol 3 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Yuri Kifer
Keyword(s):  
Dynamical Systems ◽  
Metric Spaces ◽  
Invariant Sets ◽  
Characteristic Exponents ◽  
Smooth Case

AbstractWe introduce for dynamical systems in metric spaces some numbers which in the case of smooth dynamical systems turn out to be the maximal and the minimal characteristic exponents. These numbers have some properties similar to the smooth case. Analogous quantities are defined also for invariant sets.

scholarly journals Invariant Sets in Quasiperiodically Forced Dynamical Systems

2020 ◽  
Vol 19 (1) ◽  
pp. 329-351
Author(s):  
Yoshihiko Susuki ◽  
Igor Mezić
Keyword(s):  
Dynamical Systems ◽  
Invariant Sets

scholarly journals Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant

2011 ◽  
Vol 21 (1) ◽  
pp. 013116 ◽  
Author(s):  
Eric Forgoston ◽  
Lora Billings ◽  
Philip Yecko ◽  
Ira B. Schwartz
Keyword(s):  
Dynamical Systems ◽  
Invariant Sets ◽  
Stochastic Dynamical Systems ◽  
Almost Invariant Sets

scholarly journals Topological bifurcations of minimal invariant sets for set-valued dynamical systems

2015 ◽  
Vol 143 (9) ◽  
pp. 3927-3937 ◽  
Author(s):  
Jeroen S. W. Lamb ◽  
Martin Rasmussen ◽  
Christian S. Rodrigues
Keyword(s):  
Dynamical Systems ◽  
Invariant Sets

NOISE-INDUCED CHAOS: A CONSEQUENCE OF LONG DETERMINISTIC TRANSIENTS

2008 ◽  
Vol 18 (02) ◽  
pp. 509-520 ◽  
Author(s):  
TAMÁS TÉL ◽  
YING-CHENG LAI ◽  
MÁRTON GRUIZ
Keyword(s):  
Dynamical Systems ◽  
Dynamical Model ◽  
Invariant Sets ◽  
Transient Chaos ◽  
Weak Noise ◽  
Fractal Properties ◽  
Deterministic Dynamical Systems ◽  
Chaotic Transients ◽  
Noise Phenomenon

We argue that transient chaos in deterministic dynamical systems is a major source of noise-induced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractality. The existence of a deterministic nonattracting chaotic set, and of chaotic transients, underlying noise-induced chaos is illustrated by examples, among others by a population dynamical model.

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